1. If you reflect a graph in the x-axis then you are simply taking whatever answer you get for y, and turning it to -y.

So y(x)=x³ becomes

-y(x)=x³ => y(x) = -(x³)

2. Reflecting a graph in the y-axis swaps around the values of x with the values of -x. So y(-x) = x³ => y(x) = (-x)³

In this case both of the answers are the same.